UPDATE: Serge A. Levin
has updated my jailbreak to remove the need for the precise timing, so it's no longer "temporary". If you are already jailbroken, you don't need to do anything, but if the old 3.2.1 jailbreak doesn't work or you can't get the timing right, try the new version: http://yifan.lu/2011/09/01/kindle-3-...lbreak-update/
I never planned to release a 3.2.1 jailbreak, but I see more and more people asking for it and I heard that Amazon ships 3.2.1 on non-ad kindles now. I'm not ready to release the planned jailbreak as Amazon is slowly closing all the holes so we don't need to play our best hand yet, so here's a "temporary" solution until I release the next jailbreak at the next major Kindle update.
The reason why I call it a temporary jailbreak is because it requires some precise timing. You need to run the update IMMEDIATELY after restarting in order for it to work. I've included some very detailed directions in the readme, but it may still take a few tries (which is bothersome because each try requires another restart).
I only tested it on a Kindle 2 running 3.2.1, so I may not have coded the timings right, therefore if it doesn't work in 3 or so tries, stop and tell me.
More information and download here